Nuprl Lemma : RankEx4_Foo_wf
∀[foo:ℤ + RankEx4()]. (RankEx4_Foo(foo) ∈ RankEx4())
Proof
Definitions occuring in Statement :
RankEx4_Foo: RankEx4_Foo(foo),
RankEx4: RankEx4(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
RankEx4: RankEx4(),
RankEx4_Foo: RankEx4_Foo(foo),
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
RankEx4co_size: RankEx4co_size(p),
RankEx4_size: RankEx4_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
RankEx4co-ext,
subtype_rel_union,
RankEx4_wf,
RankEx4co_wf,
ifthenelse_wf,
eq_atom_wf,
add_nat_wf,
false_wf,
le_wf,
RankEx4_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
has-value_wf-partial,
RankEx4co_size_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
hypothesisEquality,
applyEquality,
thin,
sqequalHypSubstitution,
isectElimination,
intEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
instantiate,
universeEquality,
unionEquality,
voidEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
unionElimination,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[foo:\mBbbZ{} + RankEx4()]. (RankEx4\_Foo(foo) \mmember{} RankEx4())
Date html generated:
2016_05_16-AM-09_04_11
Last ObjectModification:
2015_12_28-PM-06_48_47
Theory : C-semantics
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